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Counting Rational Points on K3 Surfaces | | David McKinnon
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2 Mar 1999 | | Subject: | Algebraic Geometry; Number Theory | math.AG math.NT | | Abstract: | For any algebraic variety $V$ defined over a number field $k$, and ample height function $H$ on $V$, one can define the counting function $N_V(B) = #{Pin V(k) mid H(P)leq B}$. In this paper, we calculate the counting function for Kummer surfaces $V$ whose associated abelian surface is the product of elliptic curves. In particular, we effectively construct a finite union $C = cup C_i$ of curves $C_i$ on $V$ such that $N_{V-C}(B)ll N_C(B)$; that is, $C$ is an accumulating subset of $V$. In the terminology of Batyrev and Manin, this amounts to proving that $C$ is the first layer of the arithmetic stratification of $V$. | | Source: | arXiv, math.AG/9903013 | | Services: | Forum | Review | PDF | Favorites | |
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